A/Prof Zihua Guo

Research Overview

My main interest lies in the field of Analysis and PDEs:

1) developing harmonic analysis tools that are motivated by PDE problems;

2) developing the understanding of the solutions to the nonlinear PDEs of dispersive types (such as Schrodinger equation, KdV equations) and PDEs arising in fluid dynamics (such as Euler, Navier-Stokes equations).

Selected Publications

[1] Guo, Zihua ; Nakanishi, Kenji. "The Zakharov system in 4D radial energy space below the ground state". In: American Journal of Mathematics. 2020 ; to appear.

[2] Cho, Yonggeun ; Guo, Zihua ; Lee, Sanghyuk. "A Sobolev estimate for the adjoint restriction operator". In: Mathematische Annalen. 2015 ; Vol. 362, No. 3-4. pp. 799 - 815. https://doi.org/10.1007/s00208-014-1130-7

[3] Guo, Zihua ; Nakanishi, Kenji ; Wang, Shuxia. "Global dynamics below the ground state energy for the Zakharov system in the 3D radial case". In: Advances in Mathematics. 2013 ; Vol. 238. pp. 412 - 441. https://doi.org/10.1016/j.aim.2013.02.008

[4] Guo, Zihua ; Kwon, Soonsik ; Oh, Tadahiro. "Poincare-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS". In: Communications in Mathematical Physics. 2013 ; Vol. 322, No. 1. pp. 19 - 48. https://doi.org/10.1007/s00220-013-1755-5

[5] Guo, Zihua ; Wang, Baoxiang. "Global well-posedness and inviscid limit for the Korteweg-de Vries-Burgers equation". In: Journal of Differential Equations. 2009 ; Vol. 246, No. 10. pp. 3864 - 3901. https://doi.org/10.1016/j.jde.2009.03.006